The Main SkyClub in Concourse A is your best bet. Showers are open to all, subject to a wait list, but the usual busy times are with the Asia arrivals. You sign up with the agents on the second floor. 10 hours is a very long time at DTW and yet there is nothing super close that I could recommend exiting the airport (maybe the Henry Ford museum in Dearborn, but...). I'd see if an earlier LAS-DTW is available that gives you 2-3 hours in DTW. If you do plan to take the red eye, I think the Westin is a very good idea.

If you are stuck with the 1 hour connection, consider requesting wheel chair support. The wheel chair attendants at DTW are very good and are almost always waiting at the plane's door to whisk their passengers to their next flight.

Have a great trip!